Lt36. 有效的数独

36. 有效的数独

请你判断一个 9x9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。

1. 数字 1-9 在每一行只能出现一次。
2. 数字 1-9 在每一列只能出现一次。
3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）

数独部分空格内已填入了数字，空白格用 ‘.’ 表示。
注意：

• 一个有效的数独（部分已被填充）不一定是可解的。
• 只需要根据以上规则，验证已经填入的数字是否有效即可。

​

示例 1：
输入：board = [[“5”,”3”,”.”,”.”,”7”,”.”,”.”,”.”,”.”] ,[“6”,”.”,”.”,”1”,”9”,”5”,”.”,”.”,”.”] ,[“.”,”9”,”8”,”.”,”.”,”.”,”.”,”6”,”.”] ,[“8”,”.”,”.”,”.”,”6”,”.”,”.”,”.”,”3”] ,[“4”,”.”,”.”,”8”,”.”,”3”,”.”,”.”,”1”] ,[“7”,”.”,”.”,”.”,”2”,”.”,”.”,”.”,”6”] ,[“.”,”6”,”.”,”.”,”.”,”.”,”2”,”8”,”.”] ,[“.”,”.”,”.”,”4”,”1”,”9”,”.”,”.”,”5”] ,[“.”,”.”,”.”,”.”,”8”,”.”,”.”,”7”,”9”]] 输出：true
示例 2：
输入：board = [[“8”,”3”,”.”,”.”,”7”,”.”,”.”,”.”,”.”] ,[“6”,”.”,”.”,”1”,”9”,”5”,”.”,”.”,”.”] ,[“.”,”9”,”8”,”.”,”.”,”.”,”.”,”6”,”.”] ,[“8”,”.”,”.”,”.”,”6”,”.”,”.”,”.”,”3”] ,[“4”,”.”,”.”,”8”,”.”,”3”,”.”,”.”,”1”] ,[“7”,”.”,”.”,”.”,”2”,”.”,”.”,”.”,”6”] ,[“.”,”6”,”.”,”.”,”.”,”.”,”2”,”8”,”.”] ,[“.”,”.”,”.”,”4”,”1”,”9”,”.”,”.”,”5”] ,[“.”,”.”,”.”,”.”,”8”,”.”,”.”,”7”,”9”]] 输出：false 解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例 1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在, 因此这个数独是无效的。
​

提示：

• board.length == 9
• board[i].length == 9
• board[i][j] 是一位数字或者 ‘.’

思路

按题意，先判断水平和竖直是否都符合，再逐个判断九个宫格是否都符合要求即可。

解答

/**
 * @param {character[][]} board
 * @return {boolean}
 */
var isValidSudoku = function (board) {
  const vertical = (j) => {
    let flag = true;
    const set = new Set();
    for (let i = 0; i < board.length; i++) {
      const element = board[i][j];
      if (element === ".") continue;
      if (set.has(element)) return false;
      set.add(element);
    }
    return flag;
  };

  const horizontal = (i) => {
    let flag = true;
    const set = new Set();
    for (let j = 0; j < board[i].length; j++) {
      const element = board[i][j];
      if (element === ".") continue;
      if (set.has(element)) return false;
      set.add(element);
    }
    return flag;
  };

  const checkGrid = (i, j) => {
    let flag = true;
    let offsetX = i * 3,
      offsetY = j * 3;
    const set = new Set();
    for (let i = 0; i < 3; i++) {
      for (let j = 0; j < 3; j++) {
        const element = board[i + offsetX][j + offsetY];
        if (element === ".") continue;
        if (set.has(element)) return false;
        set.add(element);
      }
    }
    return flag;
  };

  const check = (i) => {
    return vertical(i) && horizontal(i);
  };

  for (let i = 0; i < board.length; i++) {
    if (!check(i)) return false;
  }
  for (let i = 0; i < 3; i++) {
    for (let j = 0; j < 3; j++) {
      if (!checkGrid(i, j)) return false;
    }
  }
  return true;
};